Problem: What do the following two equations represent? $-x+3y = -3$ $5x-15y = 5$
Putting the first equation in $y = mx + b$ form gives: $-x+3y = -3$ $3y = x-3$ $y = \dfrac{1}{3}x - 1$ Putting the second equation in $y = mx + b$ form gives: $5x-15y = 5$ $-15y = -5x+5$ $y = \dfrac{1}{3}x - \dfrac{1}{3}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.